Wood for guitars / Mechanical and Acoustical Properties:
Violins produced by Antonio Stradivari (1644 – 18 December 1737) during the late 17th and early 18th centuries are reputed to have superior tonal qualities. Dendrochronological studies show that Stradivari used Norway spruce that had grown mostly during the Maunder Minimum, a period of reduced solar activity when relatively low temperatures caused trees to lay down wood with narrow annual rings, resulting in a high modulus of elasticity and low density. The Maunder Minimum (also known as the prolonged sunspot minimum) is the name used for the period starting in about 1645 and continuing to about 1715 when sunspots became exceedingly rare, as noted by solar observers of the time. During one 30-
We have long known that wood qualities vary tremendously within the same species, but assumed that much of that variation was due to mixing various age classes and log qualities of timber in the output of a typical commodity sawmill. But when experts started running tests on the tone wood which were produced, that was known to come from high quality logs and was carefully quarter sawn and air dried, they discovered the same variations in quality found in commodity lumber.
There are three easily measurable properties that affect the ability of a wood plate to vibrate: The average density of the wood, the stiffness of the wood, and the amount of vibrational damping, or losses to internal friction. In addition because of the way wood is produced as the tree grows, with the new growth laid down just underneath the bark in alternating rings of soft early growth and hard late growth, the stiffness varies depending on the orientation with respect to the growth rings (parallel, perpendicular, or tangential). Wood tests should always include measurements of longitudinal stiffness (parallel to the grain) and perpendicular, or cross-
Wood density for instruments tops (plate) is determined by weighing the test sample and by dividing its weight by its volume. The stiffness is determined by two methods: Measuring the deflection of the plate when placed under a load of known force (usually an accurately weighed steel bar), and also by measuring the fundamental vibrational resonances of the plate. The stiffness is then determined by calculating the Modulus of Elasticity from the density, size, and deflection of the plate in the case of the static load method, or using the fundamental resonance frequency in the case of the vibrational method. The acoustical damping is determined by measuring the "Q" factor, or half-
Variations on the order of 10% to 20% in densities and Moduli of Elasticity are common, even from wood samples taken from a relatively small geographic area. As the density goes up, the stiffness goes up too. But this is strictly a statistical relationship, and does not mean that a light piece of wood will necessarily be less stiff than a denser piece of wood. The Engelmann spruce is above the line of the average woods for tops (which represents the best fit of the stiffness/density relationship for these three species) for the longitudinal stiffness/density ratio, but is below the line in cross grain stiffness/density. In other words, the spruce is relatively stiffer for its weight along the grain than the red cedar and the Doug fir, but is more flexible than the other two species across the grain. Both directions of stiffness are important in a good soundboard, but the relative importance of each is still an open question. However, if we multiply the parallel Modulus of Elasticity by the perpendicular Modulus, and divide by the density (and also divide by 10**16 to get a reasonable number for presentation purposes) we get a number that gives equal weight to both directions of stiffness and the density, and hopefully allows us to better compare the absolute stiffness/density ratios of different woods in a way that is useful to judge performance as a soundboard resisting the stress of string pressure.
Even though the range and sophistication of musical instruments has increased significantly, particularly during the last four centuries or so, the range of materials from which the instruments of all these classes are manufactured has changed remarkably little. Whenever music is made by hand, whatever the location and culture, from folk to classical, from jazz to rock and pop or gypsy music, the vital parts in most musical instruments are still made from natural materials and primarily from wood, despite the arrival of sophisticated alloys, polymers, and composites. There are a number of good reasons why this is so, as will be illustrated. We begin with a brief description of the composition and structure of wood that give it its exceptional mechanical and acoustical properties.
One feature that sets wood apart from most manmade materials is that it is an orthotropic material, meaning that it has unique and independent mechanical properties in the directions of three mutually perpendicular axes: longitudinal, radial, and tangential. The longitudinal axis (L) is defined as parallel to the fiber (grain), thus along the length of a tree trunk; the radial axis (R) is perpendicular to the growth rings; and the tangential axis (T) is perpendicular to the grain but tangent to the growth rings. This orthotropy is due to the cellular structure of wood. Wood is primarily composed of hollow, slender, spindle-
Wood is a hierarchically structured composite. The cell walls consist of cellulose microfibrils embedded in a lignin and hemicellulose matrix in which minor amounts (5–10%) of extraneous extractives (e.g., oils) are contained. Variations in the volume and chemistry of these ingredients, combined with differences in the amount and distribution of porosity, determine the structure and thus the density and mechanical properties of a wood. While the properties of a single wood species are constant within limits, the range of properties among species can be large. Worldwide, the density of wood ranges from about 100 kg/m3 for balsa (Ochroma pyramidale) to about 1400 kg/m3 for lignum vitae (Guaicum officinale) and snakewood (Brosimum guianense), a value close to that of carbon-
Physical and mechanical properties of wood:
Many physical and mechanical properties of wood are correlated with density. Young's modulus and density are almost linearly correlated (regression coefficient of almost1). The Young's and shear moduli parallel and perpendicular to the grain of this orthotropic material are among these and have been shown to be important for musical plate vibration. Lacking complete sets of measurements of these moduli for woods used in musical instruments, we concentrate on the Young's modulus parallel to the grain because it has been determined for a large number of wood species and because the Young's modulus, together with the wood's density, determines most acoustical properties of a material. Additionally, the side hardness is important whenever wood carries contact or impact loads, as is the case in xylophones, for example. For clear, straight-
Another important feature peculiar to wood and important for musical instruments is that it reacts and adapts to the environmental conditions to which it is exposed, particularly that it exchanges moisture with air. Material properties that are critical for the acoustical performance of a wood such as density, Young's modulus, damping, and shrinkage are highly dependent upon the wood's moisture content. Thus, important criteria during the material selection process are also how much and how quickly a wood exchanges moisture with the environment and how the moisture affects its dimensional stability and mechanical properties. In general, the speed of moisture sorption decreases with increasing density and content of extractives. The rate and amount of water uptake along with the dimensional stability of wood can further be controlled through treatments with waxes or oils.
Acoustical properties of wood:
The acoustical properties of wood, such as the volume, quality, and color of the soundboards are determined by the mechanical properties of the material from which they are made because the sound is produced by vibrations of the material itself. The properties on which the acoustical performance of a material depends are primarily its density, Young's modulus, and loss coefficient. They determine the speed of sound in a material, the eigenfrequencies of a wooden bar, and the intensity of the radiated sound. The most important acoustical properties for selecting materials for sound applications, such as musical instruments, are the speed of sound within the material, the characteristic impedance, the sound radiation coefficient, and the loss coefficient: The speed, c, with which sound travels through a material, is defined as the root of the material's Young's modulus, E, divided by the material's density, ρ: Incidentally, this ratio, which describes the speed of longitudinal waves in a material, also characterizes the transverse vibrational frequencies of a bar. The impedance, z, of a material, is defined as the product of the material's speed of sound, c, and its density, ρ: The sound radiation coefficient, R, of a material, is defined as the ratio of the material's speed of sound, c, to its density, ρ: The loss coefficient, η, measures the degree to which a material dissipates vibrational energy by internal friction. Other measures of damping include the quality factor, Q, the logarithmic decrement, δ, and the loss angle, ψ. For excitation near resonance and small damping, these quantities are related.
Speed of sound:
The speed of sound is directly related to the modulus of elasticity and density. It is roughly independent of wood species, but varies with grain direction. The transverse Young's modulus of wood is only between 1/20 to 1/10 of the longitudinal; consequently, the speed of sound across the grain is only c. 20 to 30% that of the longitudinal value. Generally, the speed of sound in wood decreases with an increase in temperature or moisture content and proportionally to the influence of these variables on Young's modulus and density. It decreases slightly with increasing frequency and amplitude of vibration (Wood Handbook, 1999).
Like the speed of sound, the characteristic impedance is directly related to the modulus of elasticity and density of a material. This quantity is important when vibratory energy is transmitted from one medium with impedance z1 to another with impedance z2. The first medium could be a string and the second the soundboard of a musical instrument. The ratio of the reflected sound intensity, Ir, to the incident intensity, I0, can be expressed as a function of the impedances of the two media:
From these equations, we see that the transmitted intensity goes to zero if there is a large mismatch between z1 and z2, thus either z1 << z2 or z2 << z1 (Fletcher and Rossing, 1991).
The soundboard's impedance is proportional not only to the characteristic impedance of the material from which it is made, but also to the square of the soundboards thickness. As a result, soundboards with considerable thickness, such as that in pianos, for example, have an impedance significantly larger than that of the strings. To achieve a high sound quality, the impedances of the strings and the soundboard must thus be controlled very carefully. This is not a trivial undertaking, because two conflicting requirements must be met: sufficient vibratory energy must be transmitted from the string to the soundboard to make the strings vibrate audibly, while the energy should not be transmitted too readily or too rapidly, causing the vibrations of the string to die down quickly and their sound to resemble that of a thud.
Sound radiation coefficient:
The sound radiation coefficient describes how much the vibration of a body is damped due to sound radiation. Particularly in the case of soundboards, a large sound radiation coefficient of the material is desirable if we wish to produce a loud sound. To maximize loudness, we need to maximize the amplitude of the vibrational response of the soundboard for a given force, a quantity that is described by the frequency response function.
If we wish to maximize the peak response of a soundboard or a bar, rather than the average response, we need to maximize the ratio of the sound radiation coefficient to the loss coefficient, η. In soundboard design, this means that the one that radiates the loudest sound also is the stiffest per unit mass, thereby ensuring that the thin top plates of violins, which typically are only 2–3 mm thick, can support the 70 to 90 N (c. 7 to 9 kg) load of the strings with minimal deflection.
When a solid material vibrates, it is strained and some of its mechanical energy is dissipated as heat by internal friction. The mechanism by which this occurs in wood is complex and depends on the temperature and moisture content within a sample and on the type and amount of extractives characteristic for the wood species. The value of the loss coefficient ranges from about 0.1 for hot, moist wood to about 0.002 for air-
Pitch and timbre of sound:
The loudness or intensity of a sound depends on the square of the amplitude of the vibration, as described earlier. The pitch of sound of a musical instrument is determined by the spectrum of frequencies it radiates and transmits into the air. Each body has its own particular set of eigenfrequencies defined by the size of the vibrating body, the material from which it is made, and in the case of strings, on its tension. The timbre and quality of the sound that a vibrating body produces is due to the presence of eigenfrequencies, also termed overtones or upper partials, and their relative strengths. Which overtones of a sounding body are excited depends on what causes the body's vibrations: whether it is hit by a soft or a hard mallet and whether the vibration is caused by a plucked or a bowed string. The harmonics also depend on the shape of the body and on the material from which the body is made, as is explained next.
When we plot the various physical and mechanical properties and acoustical quantities described earlier against one another for the woods commonly used for different types of instruments, we can illustrate the design requirements for these instruments and analyze why certain species are especially suited for particular sound applications and therefore traditionally chosen by musical instrument makers. Woods for soundboards stand out. They have both an exceptionally high speed of sound and a remarkably high sound radiation coefficient. Woods for soundboards have both a high average and a high peak response and have an exceptionally low loss coefficient.
Woods for soundboards:
The sound that a single plucked or bowed string produces is barely audible because one string sets only a small volume of air into motion. To produce sounds with satisfactory volume for our ears, the string must be coupled to a resonator, which has a better coupling to air to transmit the vibratory energy of the string and radiate the sound. In the violin family, the string is coupled via the bridge to the top plate of the instrument, the soundboard, which usually is a piece of softwood with the grain running parallel to the strings. The bridge transmits the vibrations of the string to the soundboard, which is connected to the back plate by the sound post and the ribs. The back plate is part of the vibrating structure and as such also contributes to radiating the sound. The shape and material of the body strongly influence the sound quality and the way in which it is radiated into the room. The f-
A closer look not only at the holes in the top plates of string instruments, but also at their overall shape reveals a feature common to almost all wooden musical instruments: both the instrument itself and the holes cut into it are either round or composed of arcs. Such instrument design is not only aesthetically pleasing, but it is also prescribed by the orthotropic nature of wood. The softwoods commonly used for soundboards, such as spruce, very readily split parallel to the grain, particularly when they have the shape of a plate and a modest thickness of 2–3 mm, as is typical for violin and guitar soundboards. By cutting curves and circles, the instrument maker avoids creating the stress concentrations associated with sharp corners.
Common beliefs are that regular playing and aging of wood improve the acoustical properties of musical instruments, that instruments that are exhibited in museums rather than played lose their quality, that "old fiddles sound sweeter," and that new ones need to be "played-
Other research shows that the gradual decomposition and loss of hemicellulose with time lowers a wood's density without affecting its Young's modulus (Bucur, 2006). This avenue is being pursued further in current research to "age" soundboard wood by infecting it with a carefully selected fungus to lower the density at a constant Young's modulus and thereby improving the sound radiation coefficient and quality of the soundboards (Zierl, 2005). Further research on the "playing-
Over the millennia, we have learned to use wood to its best advantage in musical applications. The musical instruments we know today are the result of the simultaneous optimization of material and shape for the expectations of musicians and audiences at a given time and in a given culture. Despite much scientific effort to illuminate the properties of universally accepted perfect instruments and their reproduction, we still rely mainly on the art, knowledge, and experience passed on from one generation of skilled instrument makers to the next. They have the expertise to judge the quality of the material for an instrument using eye, ear, and touch—and this often when it is still hidden in the trunk of a tree or in wooden planks.
The aim of this contribution is to illustrate the unique range and combination of mechanical and acoustical properties of wood, which still make it the material of choice for musical instruments and the lining of concert halls. Material property charts that plot acoustic properties such as the speed of sound, the characteristic impedance, the sound radiation coefficient, and the loss coefficient against one another for various woods are used to illustrate and explain why spruce is the preferred choice for soundboards.